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LibrePilot/matlab/ins/LLA2NED_symbolic.m
James Cotton 0eedaa1250 Change how we convert LLA to NED. Now it is done with a taylor expansion
around the home LLA coordinate to avoid the conversion into ECEF coordinates.
This has the benefit of not requiring double precision math and uses less
operations.

Now we should remove the Rne and ECEF fields from HomeLocation as they are
unused
2012-04-03 03:42:25 -05:00

43 lines
1.2 KiB
Matlab

function NED = LLA2NED_symbolic(lla, home)
DEG2RAD = pi / 180;
a = 6378137.0; % Equatorial Radius
e = 8.1819190842622e-2; % Eccentricity
lat = home(1) / 10e6 * DEG2RAD;
lon = home(2) / 10e6 * DEG2RAD;
alt = home(3);
delta = (lla - home);
delta(1:2) = delta(1:2) / 10e6 * DEG2RAD;
delta = reshape(delta,[],1);
N = sym('a / sqrt(1.0 - e * e * sin(lat) * sin(lat))'); %prime vertical radius of curvature
ECEF = [sym('(N + alt) * cos(lat) * cos(lon)'); ...
sym('(N + alt) * cos(lat) * sin(lon)'); ...
sym('((1 - e * e) * N + alt) * sin(lat)')];
ECEF = subs(ECEF, 'N', N);
ECEF = subs(ECEF, 'e', 0);
ECEF = subs(ECEF, 'a', a);
J = [diff(ECEF,'lat') diff(ECEF,'lon') diff(ECEF,'alt')];
Rne(1,1) = sym('-sin(lat) * cos(lon)');
Rne(1,2) = sym('-sin(lat) * sin(lon)');
Rne(1,3) = sym('cos(lat)');
Rne(2,1) = sym('-sin(lon)');
Rne(2,2) = sym('cos(lon)');
Rne(2,3) = 0;
Rne(3,1) = sym('-cos(lat) * cos(lon)');
Rne(3,2) = sym('-cos(lat) * sin(lon)');
Rne(3,3) = sym('-sin(lat)');
ccode(simplify(Rne * J))
NEDsymb = simplify(Rne * J) * delta;
NED = subs(subs(subs(NEDsymb,'lat',lat),'lon',lon),'alt',alt);
%delta = subs(subs(subs(J * delta,'lat',lat),'lon',lon),'alt',alt)
%Rne = subs(subs(subs(Rne,'lat',lat),'lon',lon),'alt',alt)